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You ignored my comment about the paragraph you added to the introduction. Your text was about a very important point, and in my opinion its content was very useful, and I am glad you proposed to add it to the article. However, if you compare your text with the version I edited a few minutes ago, you will immediately understand how many sentences in that paragraph were sloppily written and how many logic steps (which I am sure for you were obvious) were not explained to the reader. A clear conclusion was also missing. You edited an A class article, and your text looked like a quick comment by an unexperienced writer on a talk page. You repeatedly showed that you can do much better. So, I assume you were in a hurry. Please do not edit articles (especially highly rated articles) when you are in a hurry, and please do not ignore what I write.
By the way, I think this article, as it is now, is too badly structured to deserve the A class. Paolo.dL (talk) 11:50, 13 July 2008 (UTC)
This paragraph was inserted by you in the introduction! I asked you to make it clearer. Since you ignored my request, I just made it clearer in all respects, and added a clear conclusion which in your version was missing, as the following comparison shows. Moreover, in my edit summary I wrote that it did "not necessarily belong in the introduction". Now you rewrote it in another section, and completely ignored my work. You behave as if you were the owner of the page.
Brews ohara | Paolo.dL |
---|---|
In a frame that rotates about a fixed axis, ... | In a frame that rotates about a fixed axis, ... |
In non-inertial reference frames that are more complex than rotation about a fixed axis, the fictitious forces take on different behaviors. (For a discussion of more complex rotations, see Euler angles.) | When the reference frame rotates about an axis which is not fixed, the fictitious forces take on a more complex behavior. (For a discussion of complex rotations, see Euler angles.) |
As a simple example of different behavior, consider general planar motion of a particle along a curvilinear path. | As a simple example, consider general planar motion of a particle at constant speed along a snake-shaped path (that is, a curvilinear but not circular planar path). |
Let L be a local and non-inertial reference frame the origin of which is attached to the particle, and which rotates to keep its xL and yL axes always perpendicular and tangent to the trajectory of the particle (see local coordinates). Namely, if we observe L from an inertial frame, we see that the direction of xL and yL varies as the particle position changes, approximately as if L (and the particle) were attached to a tiny train truck running along a very narrow railway having the same shape as the particle trajectory. | |
In the reference frame of the moving particle (see local coordinates) the centrifugal force acts outward along the radius of curvature of the path at each position on the path. It therefore varies in direction as the trajectory changes to remain continuously normal to the path. | In frame L, the centrifugal force applied on the particle acts outward from the centre of curvature of the path at each particle position. It therefore remains continuously perpendicular to the path, i.e. parallel to xL. |
[CONCLUSION] However, the magnitude and even the sense of the centrifugal force vary with time (e.g., when the curvature is to the left, the centrifugal force has the same direction as xL, while when the curvature is to the right the centrifugal force points in the opposite direction). Thus, the centrifugal force is time-variant even though the mass and the position in L of the particle are both time-invariant. This means that, when L rotates about a non-fixed axis, the centrifugal force ceases to be a simple function of mass and position, and becomes a more complex function. | |
The Coriolis force is zero in this reference frame, because the frame is attached to the moving particle, and therefore the particle has zero velocity in this frame. (However, another object viewed from this frame can be subject to Coriolis force if it has a velocity as seen in this frame.) | Notice that the Coriolis force acting on the particle is zero in L, because the particle has zero velocity in this frame. |
Aren't there policies in Wikipedia against this kind of behaviour? Paolo.dL (talk) 17:17, 13 July 2008 (UTC)
Even if you were the author of every single word in this article, this would not excuse you. I value your work and pictures, but you should respect the work of others, and you cannot write on this talk page that the paragraph was not clear and not good for the introduction, when (1) you put it in the introduction and (2) my revision was much clearer than yours. And more importantly, you cannot rewrite from scratch a text that you inserted yourself, just because somebody else edited it. Imagine what would happen if others did the same with your work. Paolo.dL (talk) 17:49, 13 July 2008 (UTC)
It does not address my concern because you rewrote it from scratch. Paolo.dL (talk) 18:11, 13 July 2008 (UTC)
At present the article states "the centrifugal force does not depend only on the mass and position of the object". This remark could be made more helpful. There is no suggestion as to what the other dependencies might be, and no reference to further discussion. In the case of general curvilinear particle motion using a local coordinate system, the statement is incorrect. I have seen no discussion for a general rigid body, so I do not know if it is a correct statement in that case. (it seems very likely to be true, because the orientation angles must enter.) I wonder if any references could be provided? Brews ohare (talk) 18:38, 13 July 2008 (UTC)
Paolo: The centrifugal force does not vanish. You could answer your questions by looking at the modified section on local coordinates and looking at the link to the book referenced. (The relevant portion is on-line at googlebooks at the link). Brews ohare (talk) 19:25, 13 July 2008 (UTC)
Here's the simplest possible example in which I am not sure anymore about the correct definition of the centrifugal force: a reference frame which is rotating at constant angular velocity about a fixed axis which does not coincide with its origin. For instance, a local frame attached to a car moving along a circular path, with its origin sitting at the center of mass of the car driver, not at the center of the circular path. The driver is at rest in this frame (null linear and angular velocity and null linear and angular acceleration), thus the net force (fictitious+real) must be zero. Questions:
Paolo.dL (talk) 20:22, 13 July 2008 (UTC)
I have not clear ideas about this (although I have a best guess). My doubt is about the correct definition of centrifugal force in the gereral case. But my example is extremely simple. Can you all give me your opinion? I believe it is important. Whatever is the correct answer, changes must be made in the article accordingly. Thanks. Paolo.dL (talk) 20:42, 13 July 2008 (UTC)
Brews suggested "maybe it's time to do some math, eh?". My suggestion is to read with more attention before answering (it would enormously facilitate our discussions). My questions were extremely clear and simple: this is just a matter of terminology. Nobody doubts that a fictitious force exists in this case and everybody knows how to compute it!
Anyway, I am glad that WolfKeeper, Brews, PeR and Wikipedia (as Brews pointed out) agree to call this fictitious force "centrifugal force". This supports my initial thesis. FyzixFighter wrote above (14:08 13 July 2008): "the centrifugal force in frame L acting on the particle is always zero since the position vector is always zero", but he probably changed his mind after reading my answer (14:51, 13 July 2008). If someone still disagrees, please let us know as soon as possible. I would love to be able to write again: "agreement reached". (not ignoring PeR's interesting point; I will discuss it later). Paolo.dL (talk) 18:11, 15 July 2008 (UTC)
As a related example, suppose the moving coordinate system B rotates in a circle of radius R about the fixed origin of inertial frame A, but maintains its coordinate axes fixed in orientation, as in Figure 3. The acceleration of an observed body is now:
where the summations are zero inasmuch as the unit vectors have no time dependence. The origin of system B is located according to frame A at:
leading to a velocity of the origin of frame B as:
leading to an acceleration of the origin of B given by:
The observers in frame B therefore must introduce a fictitious force, this time due to the acceleration from the orbital motion of their entire coordinate frame, that is radially outward away from the center of rotation of the origin of their coordinate system:
and of magnitude:
Notice that this force is a centrifugal force, but has differences from the case of a rotating frame. In the rotating frame the centrifugal force is related to the distance of the object from the origin of frame B, while in the case of an orbiting frame, the centrifugal force is independent of the distance of the object from the origin of frame B, but instead depends upon the distance of the origin of frame B from its center of rotation, resulting in the same centrifugal fictitious force for all objects observed in frame B. Brews ohare (talk) 19:48, 15 July 2008 (UTC)
PeR, I thought your position was neutral, as mine. But now I see you express a preference against the convention currently adopted by Wikipedia (which, I agree, is not a reliable source). My example (rotation about fixed axis) was simplified, Brew's example (translation about fixed axis) was even more simplified, but the real subject of this discussion was rotation about a non-fixed axis (e.g. a car along an S-shaped planar path). Please think about that, and you will see a strong reason not to use a frame attached to the center of curvature: this is by no means equivalent to the frame from which the car driver observes the world. We have two non-inertial frames (both rotating at the same speed:
These rotating frames are not equivalent, as for the observed position, velocity and acceleration of the car. They do accelerate relative to each other! In one of them, the car is of course at rest, but the center of curvature accelerates to the left or right, i.e. along the transverse axis of the car. In the other, you observe the opposite motion: the car accelerates to the right or left. This does not mean I disagree with you. Just that I find it hard to convince others that the imaginary force "experienced" by the car driver driving along an S-shaped trajectory is not centrifugal, in the driver's own natural frame of reference (i.e. his own LCS). This terminology does not seem to be based on math (math is neutral in this respect, in my opinion; you and Brews are both right about math); it seems to be also based on a philosophy and terminology which is meant to be intuitively appealing for laymen who don't have a good grasp of physics. Paolo.dL (talk) 23:31, 15 July 2008 (UTC)
Outstanding contribution, PeR. Thank you for explaining so clearly your point. I conclude that we disagree about what is wrong. Of course nobody wants to use "precise-but-wrong" concepts. Brews's opinion is that you are wrong, my opinion is that both of you are right. I agree that the only way to solve the disagreement is to quote reliable literature. By the way, the rotating frame attached to center of curvature avoids the problem without solving it. And I agree with you: "nobody would want to use this frame". The very reason why I opened a new subsection was to discuss an example in which that frame becomes completely not natural and to give you a good reason to choose the driver's subjective frame (the LCS). Paolo.dL (talk) 10:10, 16 July 2008 (UTC)
|PeR, I thought your position was neutral, as mine. But now I see you express a preference against the convention currently adopted by Wikipedia (which, I agree, is not a reliable source). My example (rotation about fixed axis) was simplified, Brew's example (translation about fixed axis) was even more simplified, but the real subject of this discussion was rotation about a non-fixed axis (e.g. a car along an S-shaped planar path). Please think about that, and you will see a strong reason not to use a frame attached to the center of curvature: this is by no means equivalent to the frame from which the car driver observes the world. We have two non-inertial frames (both rotating at the same speed:
These rotating frames are not equivalent, as for the observed position, velocity and acceleration of the car. They do accelerate relative to each other! In one of them, the car is of course at rest, but the center of curvature accelerates to the left or right, i.e. along the transverse axis of the car. In the other, you observe the opposite motion: the car accelerates to the right or left. Paolo.dL (talk) 23:31, 15 July 2008 (UTC)
This does not mean I disagree with you. Just that I find it hard to convince others that the imaginary force "experienced" by the car driver driving along an S-shaped trajectory is not centrifugal, in the driver's own natural frame of reference (i.e. his own LCS). This terminology does not seem to be based on math (math is neutral in this respect, in my opinion; you and Brews are both right about math); it seems to be also based on a philosophy and terminology which is meant to be intuitively appealing for laymen who don't have a good grasp of physics. Paolo.dL (talk) 23:31, 15 July 2008 (UTC)
Note: This section is about this figure recently added by Brews to the introduction, and removed by Paolo. Paolo.dL (talk) 18:12, 16 July 2008 (UTC)
The figure added and then removed by Paolo simply illustrates a case where the direction of an axis about which rotation is occurring is itself changing direction. This animation is a very nice illustration of a case where the analysis of the article does not apply, and is meant simply to provide a concrete illustration that there is a lot more to the problem than this article can deal with. For the general reader it is a very visual example and should be retained. In any event, the possibility of its removal is worthy of discussion here. Brews ohare (talk) 12:13, 16 July 2008 (UTC)
Paolo.dL, I have been watching this discussion page and I have got a few questions to ask you. I was blocked from editing for a month and so I wasn't able to come in to the discussion when you entered it towards the end of June.
When you first entered the discussion, my understanding was that you were advocating about three key points. However, as the discussion progressed, I lost touch with what points you were trying to make.
Am I correct in believing that you were trying to say that "actual" tangential motion of an object relative to a point origin is necessary in order to obtain centrifugal force? That is certainly the point that I was trying to make. I have been trying to tell them all that centrifugal force is not a topic which is exclusively tied up with rotating frames of reference, and that when it is so tied up, the centrifugal force term in the transformation equations only applies to objects that are constrained to co-rotate with the rotating reference frame.
These guys here seem to think that centrifugal force acts on objects that are stationary relative to a rotating frame of reference. Their belief was long ago disproved by Newton's Bucket argument yet they cite an article in a 1967 physics journal as being the definitive word on the matter.
Unfortunately, the high quality textbooks are silent on the matter. For example, Goldstein's 'Classical Mechanics' introduces the topic of rotating frames of reference. It then derives transformation equations in which the centrifugal and Coriolis terms would apply to co-rotating objects. However, Goldstein, despite the fact that all the worked examples involve co-rotation, fails to explicitly state that the equations only apply to co-rotation.
I have tried to carefully explain to these guys how the derivation makes co-rotation a prerequisite for the applicability of the equations, but my explanations are consistently ignored. They demand citations, and when I gave them one citation from a GD Scott article, they point blank refused to accept that GD Scott meant what he said.
Another important point is that these guys refuse to look at more general curved path motions. They restrict their discussion exclusively to circular motion examples in which the associated equalities mask the important details. Try introducing an elliptical motion example and they will delete it instantly. David Tombe (talk) 22:01, 17 July 2008 (UTC)
Rracecarr, I noticed while blocked that Paolo.dL had come into conflict with the majority of the editors here, and so I am now trying to get a clearer picture of what the key points of his argument are.
Meanwhile, I ought to re-iterate to you what my own main argument is. Both centrifugal force and Coriolis force are perpendicular deflections. A rotating frame of reference superimposes a circular motion on top of the already existing motion. This superimposition should not be confused with centrifugal force and/or Coriolis force.
Rotating frames of reference are a topic in applied maths that involves both centrifugal force and Coriolis force. However, centrifugal force as a topic in its own right does not need to be discussed in connection with rotating frames of reference.
Finally, the rotating frame of reference transformation equations only actually apply to objects that are physically constrained to co-rotating radial motion within the rotating frame.
You have been applying these equations wrongly in order to explain the superimposed circular motion in terms of both centrifugal force and Coriolis force. David Tombe (talk) 12:57, 19 July 2008 (UTC)
RRacecarr, centrifugal force is a radial force that can be described using polar coordinates in an inertial frame of reference.
In a rotating frame of reference, a circular motion is superimposed on top of all existing motion. If the object is stationary in the inertial frame, there will be no centrifugal force acting on it. The circular path that it appears to trace out as viewed from the rotating frame does not imply the existence of any centrifugal force. There is clearly no radial acceleration involved.
Your big mistake is in believing that this artificial circle can be constructed mathematically from a centrifugal force and a Coriolis force. It can't. I've already explained why on many occasions.
The equations that you are using to support your ideas have derivations which involve restrictions that you are deliberately ignoring. In fact, the rotating frame transformation equations are derived in exactly the same manner as are the expressions for acceleration in polar coordinates, and they lead to exactly those same expressions. From that alone, you should be able to see that Coriolis force is a purely tangential effect.
You cannot swing Coriolis force around into the radial direction and pretend that it is overriding an equally bogus centrifugal force.
The derivation involves an angular speed. That angular speed appears in the centrifugal force term and it is the angular speed of the particle under consideration. Hence the centrifugal force term only applies to particles that possess that angular speed, ie. co-rotating particles. It does not apply to particles that are sitting stationary in the inertial frame.
So you are quite wrong when you say that centrifugal force is independent of the motion of a particle in a rotating frame. The tangential motion of a particle in a rotating frame increases or slackens the radial centrifugal force.
East/West motion of air into a cyclone increases or decreases the already existing centrifugal force. But unfortunately, you have been trained to believe that these deflections of east/west motion are Coriolis force. David Tombe (talk) 17:19, 19 July 2008 (UTC)
Hi David. It's no longer true that we have only circular motion. See general planar motion. However, it is still true that I believe co-rotation is not mandatory for fictitious forces.
I'm sure long polemics can result from that remark. However, let me open by asking how you would handle the "rotating spheres" general case example. There, depending upon whether the rotating frame moves faster or slower than the actual rate of rotating of the spheres, the fictitious force can be centrifugal or centripetal. The fictitious force is mandatory to obtain the observed upon tension in the string, which is identical for all observers, inertial or otherwise.
Here is the question: how will you obtain agreement upon the measured tension if the fictitious forces go away when the spheres are at rest but the frame rotates?
How about when the frame rotates faster than the spheres, but both rotate?
How about when the frame rotates slower than the spheres, but both rotate? Brews ohare (talk) 22:55, 17 July 2008 (UTC)
"When an object moves, it will have an outward radial acceleration relative to any point origin, that is determined exclusively by its tangential speed relative to that point".
Brews, in order to obtain centrifugal force, we need to have "actual" tangential motion relative to a point origin. The question then arises as to what do we mean by "actual" tangential motion. The answer is that "actual" tangential motion is tangential motion that is referenced to the background stars.
That of course opens up more questions. But meanwhile we are left with the reality that centrifugal force is a real outward radial force that occurs on all objects that move tangentially relative to a point origin.
I will soon have an article that discusses the possible physical cause of centrifugal force. You will find it if you want to, but it won't be on these pages as it will be original research.
Getting back to the artificial circle again, there is absolutely no centrifugal force involved as there is no tangential motion involved, relative to the background stars. Your attempts to justify the superimposed circular motion mathematically in terms of centrifugal force and Coriolis force are wrong on many counts.David Tombe (talk) 13:09, 19 July 2008 (UTC)
Brews, Mutual tangential motion relative to the background stars is the accurate way to describe it. So in that case, yes I stand corrected and now accept that the motion of the origin is also relevant when we are talking about mutual tangential motion.
But in your artificial circle scenario, there is no mutual tangential motion. That has been my point all along. Without that actual tangential motion, there will be no induced outward radial acceleration. There will be no centrifugal force.
You and RRacecarr are trying to justify the artificial circle mathematically in terms of both centrifugal force and an inward radial Coriolis force. What you are doing is quite wrong. The artificial circle is a superimposition. It cannot be justified in terms of a summation of centrifugal and Coriolis force. The centrifugal force and the Coriolis force are perpendicular deflections. They are not superimpositions.
When there is no mutual tangential speed, there will be no centrifugal force.
You have been clouding up all the examples of centrifugal force by adding in the extra and unnecessary complications of considering these examples from rotating frames of reference. There is no need to do that. There will either be centrifugal force or there won't. It doesn't matter what reference frame we observe it from.David Tombe (talk) 16:57, 19 July 2008 (UTC)
Brews, Yes. Providing that we are talking exclusively about tangential motion. It is tangential motion that induces radial centrifugal force. As somebody interested in electromagnetic induction, I thought that you might have seen the connection already.
Why did you switch your interest so suddenly from electromagnetism to centrifugal force? On my part, I have been interested in the connection since I read Maxwell's 1861 paper in 2005.
It's EM induction that got me interested in centrifugal force via Maxwell's sea of molecular vortices. I notice that you were recently very interested in the meaning of the A vector and the vXB force.
Then you jumped to centrifugal force. Well you came to the right place, but I have seen no evidence yet that you have seen the connection.David Tombe (talk) 22:08, 19 July 2008 (UTC)
Brews, I fully accept that there are cases of centrifugal force which are nothing more than a mathematical artifact without any associated physical cause or physical reality. Examples of this would be the radial expansion of a line drawn between a particle moving in a straight line and a purely imaginary point origin. There are also cases of centrifugal force that would appear to have a physical cause and a physical reality. Planetary orbital theory is the prime example of the latter.
It is important that we draw a distinction between these two kinds of centrifugal force.
As regards the kind that probably does involve a physical cause, ie. planetary orbits, we are effectively in the same boat as is the case with gravity. We can do it all mathematically without consideration of any physical cause. Even Newton, who suspected aether inflow theory to be the cause of gravity, was never confident enough to make an issue of this belief. He concentrated exclusively on the mathematical description of the effect.
It gets more interesting however when we move over to magnetism. Maxwell extrapolates centrifugal force to the extent that a very real centrifugal force will repel two vortices that are aligned in their equatorial plane. According to Maxwell, this is the centrifugal force that we feel when we try to push two like magnetic poles together. That is no artifact.
That is the subject that I am currently investigating.
On the main article, there exists one very interesting section entitled 'Potential Energy'. I'm surprised that this section has survived Anome's purges. That section is perhaps the most useful section on the entire page in terms of pointing us in the direction of the underlying cause behind centrifugal force.
Now to answer your specific questions, you will have to get into the way of thinking in terms of the radial and the tangential direction. These are the only two directions that have any physical significance on the microscopic or the cosmological scale. Cartesian X, Y, Z is a language which is quite simply not suitable for the purposes of analyzing centrifugal force.
You should understand the concept of the tangential direction as a matter of course. I shouldn't have to explain it to you. If the Moon had no tangential motion relative to the background stars, it would fall to Earth radially.
Your examples about the imaginary point origin moving are examples of centrifugal force that are only mathematical artifacts.
But your artificial circle example is not even a mathematical artifact. It is nothing. It involves no centrifugal force in any shape or form, either mathematical or physical. There is no radial acceleration involved. A rotating frame of reference cannot even create a radial artifact, never mind a real centrifugal force. David Tombe (talk) 12:38, 20 July 2008 (UTC)
Brews, it sometimes leads to 'mathematical artifact' centrifugal force. The best example of mathematical artifact centrifugal force is two imaginary points moving in straight lines and possessing mutual tangential speed. There will be an induced outward radial centrifugal force acting between them. It will be mathematically real but it will possess no physical significance.
Regarding the meaning of tangential, I don't know why you insist on having to have this explained to you in terms of an x-direction. Can you not simply understand the concept in its own right?
Radial motion relates to the distance between two points. Tangential motion is perpendicular to radial motion and it induces a radial acceleration.
I'm not quite sure if you are being genuine as regards your enquiry about the meaning of tangential. It is a trivial issue which most people take for granted. You should try not to filibuster the more important issues by getting the discussion sidetracked into pedantic trivia such as discussing the meaning of 'tangential'. In doing so you are ignoring all the interesting questions such as the link between electromagnetism and centrifugal force. David Tombe (talk) 14:41, 20 July 2008 (UTC)
Brews, Tangential motion is perpendicular to radial motion. It only has any meaning when it is referenced to the background stars, because in that case it results in outward radial acceleration.
Just imagine two points passing each other but not colliding. The tangential motion is the component of the motion of each particle that is perpendicular to the line that connects the two points. The radial motion is the motion that affects the distance between the two points.
All tangential speed will be accompanied by an outward radial acceleration given by v^2/r, where v is the tangential speed and r is the distance between the two points.
That is centrifugal force in a nutshell. But it doesn't tell us very much about the underlying physics or the nature of any associated potential energy.
The underlying physics has not yet appeared in the textbooks, just as the underlying physics behind the force of gravity has not yet appeared in the textbooks. David Tombe (talk) 18:40, 20 July 2008 (UTC)
Timothy, we'll have to agree to differ there. You talk about the ramblings of Maxwell. You are overlooking the fact that he led us to the standard equations of electromagnetism that we use today. You may argue that we can obtain these same equations using relativity. Well I disagree. Maxwell and relativity don't mix. The reason why I have sided with Maxwell is because we need to have a physical explanation for the displacement current. The textbook derivation of Maxwell's displacement current is flawed. I'm sure that you would agree with the textbook derivation but there's nothing I can do about that. Don't assume that I am not familiar with relativity. The difference between you and I is that I scrutinize these things to make sure that there are no flaws in the derivations. And that gets us back to centrifugal force. You come back after a few months as if all those arguments we had about rotating frames never happened. I showed you exactly where the flaws were in your extrapolation of those equations to particles that are stationary in the inertial frame. You used every trick in the book to wriggle out of having to acknowledge those flaws. You tried to cloud the whole issue up by introducing the three body problem. You tried to cloud it up by allowing the reference point in the rotating frame to be in motion relative to the rotating frame. And now you are pulling the oldest trick in the book. You are returning as if those arguments never took place and that your own understanding of centrifugal force is perfect. David Tombe (talk) 19:09, 28 July 2008 (UTC)
And from your writings its pretty easy to deduce that you are completely unfamiliar with the contents of general relativity. Otherwise you would for one know that it in fact identifies gravity as just another inertial force, which results from using coordinates in which geodesics are not straight lines. You would also not be making silly mistakes resulting from erroneously identifying the tangent spaces of different points. So it seems very safe to assume that you have very little knowledge of general relativity. That is the true difference between you and me. I have actually understood the underlying physics, while you seem to be milling in the same confusion that the 19th century physicists were struggling with. (TimothyRias (talk) 22:15, 28 July 2008 (UTC))
[NOTE: The discussion about this topic started in a previous section. Paolo.dL (talk) 11:24, 19 July 2008 (UTC)]
Paolo has removed the following material without discussion (from which I have dropped the original figure and here's another possibility):
((cite book))
: |page=
has extra text (help), Ahmed A. Shabana (2001). Computational Dynamics. Wiley. p. p. 379. ISBN 0471053260. ((cite book))
: |page=
has extra text (help), Haruhiko Asada, Jean-Jacques E. Slotine (1986). Robot Analysis and Control. Wiley/IEEE. p. §5.1.1, p. 94. ISBN 0471830291.
I see no harm in alerting the reader to more general cases and proving links where more information can be found. It is clear that the case of a fixed axis of rotation provides a good starting point, but it is easy to get the idea that it is the only case of importance. Anybody have suggestions? Brews ohare (talk) 22:19, 18 July 2008 (UTC)
/* Scope of the article */ See talk page. This section must be rewritten. Figure shows a motion about a SINGLE FIXED axis (as the caption explains) which is totally the opposite of what it should show [NOTE: this edit summary refers to the figure showing gyroscope precession]
Brews, I warned you that the language in this reference was sloppy, and you reinserted it without even bothering to clean it up
A precession can be (and typically is) a rotation about a rotating axis. But the picture you added showed a rotation about a fixed vertical axis (i.e. a precession with same angular velocity as the rotation about the "south-north" axis of the object). |
OK, you people are obviously not interested in looking for consensus on this issue. The core group of editors on this page seems to be content to argue with each other until Hell freezes over, meanwhile you accomplish nothing. The project is not well served by these never ending circular arguments. Beeblbrox (talk) 05:48, 23 July 2008 (UTC)
Hey, you may actually have a point here worth considering. What you guys need to do is ask yourselves what the user needs to know, and stop splitting fine points that the user will never understand. I give this article an F grade because it is not written for the user to understand but for wikipedia egos.72.84.64.6 (talk) 13:09, 23 July 2008 (UTC)
I've stopped keeping continuous track of this article, but it looks to me like there is still too much argument and too little sourcing. A very good example is the edit war over the difference between "reference frame" and "coordinate system"; it would be resolved much more easily by referring to a reference than by repeated addition and removal. There also seem to be flurries of editing over very minor points, which then end up overemphasized in the article--is it possible that, this being a general-purpose encyclopedia, we could resolve some of the arguments more concisely simply by being less specific? -- SCZenz (talk) 11:08, 21 July 2008 (UTC)
It has become clear that citations will not settle the matter. The distinction between inertial frame and coordinate system spelled out in the citations still appears to Paolo to be inessential. Brews ohare (talk) 10:55, 22 July 2008 (UTC)
The root cause of all the problems on these pages lies in the fact that centrifugal force is being treated as something that only occurs in rotating frames of reference.
I did applied maths and theoretical physics at university and I used the Goldstein's classical mechanics textbook as well as Williams's 'Dynamics'.
In both those books there are two quite distinct chapters in which the subject of centrifugal force emerges. There is,
(1) Rotating frames of reference. And,
(2) Planetary orbital theory.
Centrifugal force is a subject in its own right and it doesn't have to be studied exclusively in connection with rotating frames of reference. That is what is causing all the confusion on these pages. Every time a demonstration is introduced, they all have to start rambling on about looking at it from the inertial frame and looking at it from various rotating frames. They refuse to look at centrifugal force as a phenomenon in its own right.
I have tried many times to introduce planetary orbital theory unto the main page as a means of demonstrating centrifugal force. But those edits were instantly erased on every occasion, usually on the quite dishonest grounds that I hadn't supplied any citations when in fact I had.
The problem on these pages will not be resolved until a new independent group of administrators get involved and put the likes of RRacecarr and Wolfkeeper on a lead. At the moment, those two along with a few others have enjoyed a total liberty to delete the edits of anybody who they perceive to be contradicting their own prejudices, and the administrators that have been involved so far such as SCZenz and Anome have shown themselves to be totally biased.David Tombe (talk) 11:22, 22 July 2008 (UTC)
Paolo.dL, I'm fully aware of the distinstion between the different kinds of centrifugal force including what you term reactive centrifugal force. I am most certainly not confused in that respect. Any satisfactory article about centrifugal force will ultimately have to detail all these different phenomena which come under the umbrella heading of centrifugal force.
So far I have not been getting heavily involved in debating these kinds of details.
The definition of centrifugal force as is given in this article is quite wrong. Centrifugal force is not defined exclusively in connection with rotating frames of reference. I can give you at least two quality citations from university textbooks which deal with rotating reference frames in one chapter and lead up to what they describe as the 'well known centrifugal force'. In other words, centrifugal force is something that is already understood and defined independently of rotating frames of reference.
This is corroborated by the fact that the same 'well known centrifugal force' is then mentioned again in another chapter on planetary orbital motion in a context which does not involve rotating frames of reference.
In fact orbital theory uses polar coordinates in the inertial frame.
I am finding it difficult to accurately follow your argument with Brews. It seems to me that you are arguing about coordinate frames and coordinate systems. I believe that the confusion is totally connected with the fact that matters to do with centrifugal force as would normally be dealt with using polar coordinates, are being dealt with in the article within the totally unsuitable context of rotating frames of reference.
While I was blocked in June, a new editor called TstoneT appeared. He seemed to be arguing what I am saying, that polar coordinates can be used to deal with centrifugal force independently from rotating frames.
But TstoneT has now disappeared. Nevertheless, TstoneT's comments hit a raw nerve with Wolfkeeper who stated that the article is about rotating frames and that he has no intention of changing that. Wolfkeeper has also stated in strong terms that this article is not about polar coordinates.
Wolfkeeper has got absolutely no right, or no basis in the textbooks, to demand that centrifugal force must be treated exclusively in connection with rotating frames of reference. But you will notice that there is a hierarchy amongst the group of editors here that control the article. Nobody ever crosses Wolfkeeper. Nobody crosses RRacecarr either, but not even RRacecarr will ever cross Wolfkeeper. The administrators always back up Rracecarr and Wolfkeeper.
Until that state of affairs is altered, the situation doesn't look very hopeful. David Tombe (talk) 01:12, 23 July 2008 (UTC)
Once more to make this very clear to you guys. The user is going to enter centrifual force, he is not going to know the difference between this and reactive centrifugal force. So this article will be useless to him because it doesnt discuss what he is seeking information about. You need to combine the articles and explain the difference in the one article. Otherwise you are confusing the user.72.84.64.6 (talk) 13:12, 23 July 2008 (UTC)
I made an edit to the introduction which in normal circumstances shouldn't have needed a reference because it is uncontroversial. Nevertheless I decided to put a reference in for good measure. Within five minutes of having made the edit, and while I was in the process of typing in the reference, Wolfkeeper in his normal style swooped in and deleted the edit. David Tombe (talk) 02:03, 23 July 2008 (UTC)
Wolfkeeper, the introduction does not define centrifugal force at all. As it stands now, the introduction states two major theoretical physics/applied maths topics in which centrifugal force is treated, and it gives a brief description of the effect in each case.
Nothing at all regarding rotating frames has been removed from the introduction.David Tombe (talk) 02:59, 23 July 2008 (UTC)
This is the most stupid ridiculous answer I have even read. The user doesnt enter reactive centrifugal force he enters centrifugal force. Thus he gets the wrong page, because your definition ignores what the user is thinking. This is why you guys are creating a web site that users find stupid and poorly written. You need to stop writing articles that feed your own egos, and start writing articles that users really can use. They dont care about your ego trips here in the wikipedia dream world. They want information that they can understand and use. You get an F grade on that score.72.84.64.6 (talk) 12:59, 23 July 2008 (UTC)
This is a sticky subject. There are many influences on the tides. A principle influence is the tidal force which has nothing to do with centrifugal force, but has to do with the gradient of the Moon's gravitational force. The radially outward component of this tidal force appears to be less significant than its tangential component. In addition, the centrifugal force that is operative is the centrifugal force due to rotation about the barycenter, not the about the Earth's axis of rotation. Thus, bringing this matter up is a dubious exercise as it is not a clean example of centrifugal force, but requires a great deal of background. As it is, the article on tides is a total mess and cannot come to grips with the issues involved. I'd recommend that no mention of tides be made. Brews ohare (talk) 02:56, 23 July 2008 (UTC)
Here is a little discussion to point out what we are getting into here:
Why aren't the Atlantic and Pacific coast tides the same?
Brews ohare (talk) 04:14, 23 July 2008 (UTC)
Inadequate links and discussion of this figure. How does the figure contribute to the understanding of the article? As it stands, it does not contribute. A description of Lagrange points has not been attempted and might lead the reader far off topic. Without more context, this figure should be deleted. If necessary context is too large, it also should be deleted. Brews ohare (talk) 03:15, 23 July 2008 (UTC)
Wolfkeeper, the potential energy due to centrifugal force in a gravitational field exists as a matter of fact without involving rotating frames. There's a whole page on it in Goldstein's (page 78). Centrifugal potential energy in a gravitational field is obtained by substituting Kepler's areal constant into the expression for kinetic energy and obtaining a position dependent term (inverse square law to be precise, which means that centrifugal force in a gravitational field is an inverse cube law repulsive force).
In the example given in the centrifugal potential energy section in this wikipedia article, prior to you introducing the three body problem, we are dealing with the conversion of rotational kinetic energy into other forms of potential energy. The example of the rotating water is in fact a reactive centrifugal force example in which the potential energy is associated with the pressure caused by the centripetal force that forces the water off its inertial path. It is also a point in fact however that tangential kinetic energy (or for that matter, rotational kinetic energy) is in fact the same thing as centrifugal potential energy. So the example involves centrifugal potential energy being converted into gravitational and hysrostatic potential energy.
Interstingly, if you agree with Maxwell's theory of magnetic repulsion which employs centrifugal force, then it becomes clear that magnetic repulsion does not obey the inverse square law. On summation over his molecular vortices, it may not even obey the inverse cube law. But at any rate, it becomes quite clear why we can have magnetic levitation. Earnshaw's Theorem should not be involved when considering magnetic levitation. Hence there should be no controversy.
Based on Maxwell's works, we can deduce that magnetic potential energy is in fact fine-grain centrifugal potential energy. Does that help to explain why we can have a magnetic potential energy when in fact the force law that is used to explain electromotive force, F = qvXB, allegedly has got no associated potential energy?
And does it help to explain why I deleted the bits that RRacecarr restored?
Remember, Coriolis force and the F = qvXB force are mathematically identical if not physically identical.
I'm seriously considering that Coriolis force and F = qvXB do have an associated potential energy, and as in the case of centrifugal force, it is given by grad (A.v). Goldstein's backs me up on this. In the Lagrangian chapter at page 23, they derive A.v as a Lagrangian for the F = qvXB force. And there is some on-line encyclopaedia (something like Eric Weisstein) that writes the Lorentz force using grad (A.v) for the vXB term.
But in order for it to make any physical sense, we would have to involve vorticity. In the absence of vorticity, Coriolis presure/potential energy would have to be externally applied such as would be the case in water moving radially along a pipe on a rotating turntable.
In fact, I think that we should move all references to potential energy in connection with Coriolis force off these pages completely and unto the Coriolis page page, as the matter is highly controversial. David Tombe (talk) 13:10, 23 July 2008 (UTC)
Wolfkeeper, you are a wikistalker. You are messing the whole article up out of sheer spite. We need one centrifugal force article. This article is not about rotating frames. It is about centrifugal force.
Planetary orbits are thee single most important example of centrifugal force. They determine the inertial path.
You are making a dog's dinner out of it all. You are bringing in alot of unnecesary complications about three body problems into the potential energy section while at the same time deleting all references to the two body problem.
This is because you can't understand the two body problem. Nobody can understand the three body problem and that is why you like to hide behind the three body problem. David Tombe (talk) 14:21, 23 July 2008 (UTC)
Now we are seeing the mechanisms very clearly. In order to prevent Wolfkeeper breaching the three revert rule, his ally FyzixFighet takes over. No discussion whatsoever. FyzixFighter deletes perfectly good sourced material for the sole purpose of backing up Wolfkeeper.
And the administrators let all this happen. Until such times as Wolfkeeper, RRacecarr, FyzixFigher, PeR, SCZenz, Anome, Itub, Plvekamp, and Henning Makholm are put on a tight lead, this article well remain a total dog's dinner. David Tombe (talk) 14:27, 23 July 2008 (UTC)
The equation of motion in r, with expressed in terms of l, Eq. (3.12), involves only r and its derivatives. It is the same equation as would be obtained for a fictitious one-dimensional problem in which a particle of mass m is subject to a force . The significance of the additional term is clear if it is written as , which is the familiar centrifugal force.
If we analyze the motion of the Sun-Earth system from a frame rotating with Earth, it is of course just the balance between the centrifugal effect and the gravitational attraction that keeps the Earth (and all that are on it) and Sun separated. An analysis in a Newtonian inertial frame gives a different picture. As was described in Section 3.3, the angular momentum contributes to the effective potential energy to keep the Earth in orbit.
FyzixFighter, You have admitted that you made the reversion before you had even studied the details. Your excuse about the three revert rule was nonsense. How could I have broken the three revert rule without Wolfkeeper also having broken it? That was a total rubbish reason.
Your prejudice means that nothing that you say above can be taken seriously. You have simply adopted the usual stance which you guys do when you are confronted with citations that contradict what you have been saying. Just as you denied the GD Scott reference and just as SCZenz. PeR, and Anome denied the Maxwell reference, you are playing the old trick of pretending that you see a different meaning in the reference.
It's quite clear to all unbiased observers simply from what you have written above, that centrifugal force is involved in central force orbits without recourse to rotating frames of reference. Your attempts to try and pretend that Goldstein meant otherwise were pathetic. It's just a pity that there aren't any administrators who can see right through the likes of you. David Tombe (talk) 21:21, 23 July 2008 (UTC)
David: Can you divert yourself from engagement in the social heirarchy of Wiki to answer this question asked earlier:
David: You are confusing me about what you really think about the two objects in straight-line non-intersecting motion in an inertial frame fixed to the fixed stars. On one hand, you have said that two such bodies in straight-line motion do exhibit tangential motion and will be subject to centrifugal force. Now you say they will be subject to centrifugal force only if they are also subject to centripetal force. But ... I cannot see any centripetal force occurring unless the objects are in a curved path. So, you can see my dilemma. What do you want to say?? Brews ohare (talk) 21:18, 23 July 2008 (UTC)
But in the inertial frame of the fixed stars, straight-line motion means no net force. So how can there be centrifugal force?? There is nothing to balance it, to make zero net force, because there is only one other body, also in straight line motion. The only force that body generates is centrifugal force. Sounds impossible ?.! Brews ohare (talk) 00:46, 24 July 2008 (UTC)
Brews, we don't need to introduce frames of reference at all to discuss centrifugal force. If two points possess mutual tangential speed relative to the background stars, then they will automatically possess an outward radial acceleration. The second time derivative of the distance between the two particles will be v^2/r where v is the mutual tangential speed and r is the distance between the two particles.
It is as simple as that. That is the very centrifugal force that is used in the analysis of planetary orbital motion. David Tombe (talk) 18:53, 25 July 2008 (UTC)
Brews, I agree with Newton's three laws of motion absolutely. But I think that they are better expressed in the singular form of Mach's definition of inertial mass. Mach said that the mass is inversely proportional to the induced accelerations associated with mutual interaction. In other words m1a1 = -m2a2. That is Newton's three laws all in one.
There is nothing that I have said above that contradicts Newtons laws. But I think I know what you are thinking. You see straight line motion in an intertial frame and you think of inertia and Newton's first law. You think that no forces are acting and that there is no acceleration. Then here comes me telling you that there is a centrifugal force acting radially outwards between the two particles.
Actually, my disagreement with Newton is over the issue of the existence of this centrifugal force. But if it does exist then it causes a centrifugal acceleration and hence it doesn't breach Newton's laws of motion.David Tombe (talk) 21:37, 26 July 2008 (UTC)
63.24.120.84, That was a pretty good analysis of my position. It's absolutely true that I have never been happy with the Newtonian concept of the inertial frame of reference and X,Y,Z. As I said above, I much prefer Mach's approach. I do see your point that my application of Newton's laws to a force in the radial direction is at variance with Newton's law of inertia in X,Y,Z. But then of course that applies to the centripetal force just as much as to the centrifugal force. One of my biggest problems during the height of this edit war was that my opponents would use polar coordinates for their arguments but then switch into X,Y and Z in order to sabotage centrifugal force. My argument was that planetary orbital theory is done exclusively in polar coordinates. My opponents have consistently refused to allow any mention of that topic in the main article despite my having provided very good references from standard university textbooks. In my mind, centrifugal force is the same thing as inertia but described in a different language. The logic that my opponents were using in order to deny the existence of centrifugal force was equivalent to saying that aeroplanes don't exist because in German we call it a Flugzeug. In summary, I fully support the principle of Newton's laws of motion but even to the extent of extending them into polar coordinates. If that makes me at variance with Newton's original intentions, then Brews does indeed have a point. But the modern classical mechanics textbooks are also at variance with Newton's approach to planetary orbital motion for that very reason and I was basing my own approach entirely on how I learned it at university through Goldstein's etc. I am not advocating any original research as regards centrifugal force on these pages. I am glad however to see that you have been able to identify the issues because few others have. There is another anonymous that seems to have identified the issues, and there was a username TstoneT who came here briefly in June. I think that he was on the right lines too and he suppplied some references regarding dealing with centrifugal force in polar coordinates in what he called the inertial frame. At the time, he disagreed with me but it was because of a misunderstanding regarding him talking about stationary polar coordinates in the inertial frame. His terminology confused me but I realize now that he was talking about polar coordinates and the fact that centrifugal force was a radial force. On the issue of original research, I do do original research. You said that a Machian approach had never been completed and that I should enquire into why. I have been working hard on decyphering Maxwell's molecular vortices and linking centrifugal force to magnetic repulsion. I haven't as yet encountered any problems with the particle to particle approach. Can you give me any summary of where it is believed that such an approach breaks down. David Tombe (talk) 01:36, 28 July 2008 (UTC)
Until now, I've largely ignored the discussions on this page, as it appeared that nothing terrible was happening to the article and no edit wars were breaking out. I do think that the participants in the discussion are having a general discussion about physics rather than a discussion about how to improve the article using sourced, properly referenced materials from standard texts, which is what everybody's supposed to be doing on Wikipedia. Disparaging remarks have no place here, nor does original research or analysis. This article is the subject of informal mediation as noted at the top of the page, and I strongly urge that everybody avoid endless philosophical discussion and complaints about other editors. Acroterion (talk) 14:47, 23 July 2008 (UTC)
Yes Acroterion, on the last two occasions, I was blocked for supposedly being uncivil to other editors following severe provocation. The provocation came from Wolfkeeper who was blatantly wikistalking. He broke all the rules. Meanwhile, SZCenz hung around waiting for me to show the first signs of anger and then he blocked me for one month.
I haven't noticed any of them ever getting blocked for being equally uncivil.
On the previous occasions, I was blocked on the basis of downright lies on the part of administrator Anome.
Anyway, I hope you live up to your word. I'm soon going to re-install the sourced sentence about centrifugal force in planetary orbits. I'll be looking forward to seeing you locking the page.
If you are genuine and you read what FyzixFighter wrote above, I think you will begin to understand what this edit war is really about.David Tombe (talk) 21:25, 23 July 2008 (UTC)
Acroterion, it's not much use having an administrator who openly admits that he doesn't understand the content of the dispute and who directs his complaints generally at everybody involved in the dispute. That is not how disputes are resolved.
Have you ever thought about enquiring into why this group are so determined to mask the truth regarding centrifugal force? You have seen for yourself how they denied that a marble on a rotating turntable would roll outwards along a radial groove. They denied that and deleted my edit on the matter as a result of which I got blocked for a month.
Do you not have the least curiosity to ask yourself why these people are denying such a basic fact?
You have now seen them attempting to deny the involvement of centrifugal force in planetary orbits despite the fact that I have supplied a very professional reference on the matter.
Are you not ineterested to know what is the driving force behind this corrupt behaviour coming from these young college students? I can tell you exactly what it is. These guys are uncomfortable with the fact that centrifugal force is an absolute effect. It contradicts the philosophy that they were introduced to at university that all things are only relative and that nothing is real.
That's what it's all about. It is a fanatical group of denilaists just like the other group over on the Mozart page who are in total denial of the fact that Mozart was a German despite a large number of citations which indicate the contrary.
These kind of people seem to gather together and dominate many of the pages on wikipedia. Are you one of that kind? David Tombe (talk) 01:31, 24 July 2008 (UTC)
David, these kinds of remarks are the reason you've been blocked so many times. Some of the editors you call "young college students" are experienced physicists with PhD's, who have published in reputable mainstream journals. You could learn from them if you'd listen, instead of constantly arguing with them. Their interpretation of the sources is in line with the mainstream view as required by Wikipedia's WP:NPOV, WP:RS and WP:OR policies. They have been reverting your misinterpretation of sources, and have tried to explain the material to you. Personally, I gave up on trying to discuss this with you a long time ago. Plvekamp (talk) 02:08, 24 July 2008 (UTC)
Hey, plvekamp, that is just plain wrong. Mr Tombe is correct that the editors are biased, I have seen it. You guys just dont want to see yourselves as users see you. Users see you as biased ego tripping brutish thugs who delete edits of those you dont like. You are just an unfair biased clique who dont want to straighten out your mean and nasty behavior towards users who are not members of your clique. Administrators are as bad as the others. Wikipedia is just a poorly written stupid excuse for an encyclopedia. You need to reform it so it can really be something worth while, but you are too busy ego tripping. 72.64.54.150 (talk) 16:31, 24 July 2008 (UTC)
I suggest replacing into the potential energy section the sentence: The Coriolis force has no equivalent potential, as it acts perpendicular to the velocity vector and hence rotates the direction of motion, but does not change the energy of a body. It was removed by DT because he claims it is controversial. It is not. He is the only one who thinks so. He has an original theory about potential energy of Coriolis and magnetic forces.
I would also like to add something to the section about centrifugal and gravitational potential on the surface of the earth. Here's a stab:
Calculations done in the reference frame of the earth (or any other rotating planet) can be simplified by combining the centrifugal potential with the gravitational potential. The gradient of the resulting potential function is the effective gravity, and can be treated as a single force field. It does not matter, dynamically, how much of the force is due to gravity and how much to the centrifugal effect. The equipotential surfaces of the combined potential are everywhere perpendicular to the direction of effective gravity, which is the direction shown by a plumb-bob. Mean sea level is one these equipotential surfaces.
Rracecarr (talk) 14:41, 24 July 2008 (UTC)
Racecarr, I dont understand what you mean by this. Since the article is about an apparent force and not a real force this entire topic seems to be a lot of calculations regarding a force that doesnt really exist. You guys seem very confused to me. Is this article about a real force or an apparent, fictitious force or is it about something else? You need to get clear what you are talking about in this article.72.64.54.150 (talk) 16:42, 24 July 2008 (UTC)
RRacecarr, Coriolis force does indeed act at right angles to the motion. But so does centrifugal force. Hence that cannot be used as a reason for why Coriolis force doesn't have an associated potential energy.
Furthermore, on closer examination, it is clear that centrifugal potential energy is actually just tangential kinetic energy.
In an irrotational gravity field, we can substitute the Keplerian areal constant into the centrifugal potential energy term and obtain an inverse square law position dependent expression for centrifugal potential energy. It's all on page 77 of Goldstein's. The combined gravitational potential energy and centrifugal potential energy leads to a graph just like the inter-atomic forces potential energy graph. And it is a radial effect similar to what you said above regarding combining gravity and centrifugal force into one.
In an irrotational field, Coriolis force only changes the direction of an object and so there is no potential energy involved.
But the wording in the sentence that I removed, does not accurately refelect this state of affairs. I told you at the beginning that all the facts were correct but that the reasons weren't the reasons for the facts.
I should also add that in an irrotational field, I can't think of any way of obtaining a Coriolis force apart from externally applying one, such as in the example of water flowing radially through a pipe that is fixed on a rotating turntable.
To obtain a Coriolis force naturally we would need a vortex field such as we get in magnetism. In that case we could indeed have a Coriolis potential energy simply by considering the radial kinetic energy and a gradient taken on the basis of a tangential coordinate.
It's best that this topic is taken to the Coriolis force page since is is only cluttering up an article on centrifugal force that is already top heavy with irrelevencies. David Tombe (talk) 18:42, 24 July 2008 (UTC)
It seems to me that this is exactly what Mr Tombe has been saying. Now you are saying what Mr Tombe has said. But you blocked him for saying this. So it seems you are either mistaken or just plain prejudiced against Mr Tombe. So explain why you deleted his edits when he is saying just what you say here. I think you are just confusing things, and act out of disrespect towards Mr Tombe for no real reason that makes sense to me. I certainly can see why Mr Tombe is argry with you guys, you appear to be hypocrits.72.64.54.150 (talk) 18:58, 24 July 2008 (UTC)
It always seemed to me that it was simply a matter of "prevented inertia". In other words, a ball on a string is being propelled in a straight line until the string pulls the ball off line and into the circular motion around the center.
In the instance of sitting in a car, the car turns a corner, my body wants to continue in a straight line, which it does until prevented by the door or my seatbelt, and my forward propulsion is curved off the line.
What is fictitious about that? dgaubin (talk) 16:46, 29 July 2008 (UTC)
It's a question of the language that we speak in. In X, Y, Z, it's inertia. In polar coordinates it's centrifugal force. The argument has been over whether centrifugal force is acting in a non-rotating bucket of water when it is viewed from a rotating frame of reference. When a bucket of water is really rotating, there really is a centrifugal force which causes the water to climb up the walls of the bucket. But what about a stationary bucket of water as viewed from a rotating frame of reference? The water doesn't climb up the walls of the bucket. I say that that means there is no centrifugal force. Most of the rest of the editors here say that there is a centrifugal force but that it has been over ridden by a radially inward Coriolis force that is twice as strong. David Tombe (talk) 19:27, 29 July 2008 (UTC)
It's good to avoid being dogmatic about these things, because it is, after all, just a matter of convention as to which terms arising from a non-trivial spacetime connection we choose to call "acceleration corrections" and which terms we choose to call "fictitious forces". As you said, we can learn lessons from relativity, and one of the main lessons is that physical phenomena are most naturally expressed in terms of a unified spacetime representation, rather than treating space and time on fundamentally different footings. From the spacetime point of view, there is just a single "connection", and any non-linearity of either the spatial or the temporal coordinate axes (relative to inertial worldlines) leads to correction terms. The question is what we choose to call these terms. (Of course, it doesn't really matter what we call them, but the inconsequentiality is what makes the topic so conducive to argumentation!) We could call them all corrections to our accelerations, or we could call them all fictitious-forces, or we could call some fictitious-forces and some acceleration corrections. It's really just a throwback to pre-relativistic thinking to treat the terms arising from spatially curved coordinates one way, and the terms arising from temporally curved coordinates a different way. (You can find a detailed discussion of this topic if you do a google search on "curved coordinates and fictitious forces".) It's a nice irony that Mr. Tombe, an anti-relativity zealot, was actually advocating the more sophisticated relativistic point of view here (although he didn't realize it and would probably deny it), whereas the other editors, who consider themselves to be supporters of relativity, have been doggedly defending the pre-relativistic conventions (although they don't realize it and would probably deny it). This is what makes Wikipedia so entertaining (a battle between the half-wits and the half-wise).63.24.38.196 (talk) 04:14, 2 August 2008 (UTC)
At the start of the current article there appears a list of pointers to other article, and the last item on the list says "For the scalar force that appears in polar coordinates, see the article on polar coordinates". I checked the article on polar coordinates, and the word "scalar" doesn't appear there. So, what exactly IS a "scalar force"? And why does the article point to another article for explanation of something that isn't even mentioned in the other article? Surely something is amiss.63.24.61.29 (talk) 20:48, 2 August 2008 (UTC)
I believe this pointer is better left out in the first place, or a separate discussion should be added in this article. The whole idea that the radial term in polar coordinates is a centrifugal force in any sense of the word is a stretch to begin with. Were it not for D Tombe, I doubt that this idea would ever surface. Brews ohare (talk) 16:39, 3 August 2008 (UTC)
This section is about the figure showing gyroscope precession.
I am very happy to be able to write again a section with this title. I believe we all now agree on this (please correct me if I am wrong):
Paolo.dL (talk) 21:03, 19 July 2008 (UTC)
Now, what about the new figure? Is there anybody who would like to help Brews to find a better figure? We need a figure showing a precession (for instance a twisting diver/gymnast, or the precession of a spinning top or just the previous figure modified to show the quick rotation of the gyroscope wheel, and with a different caption rewritten from scratch; any of these or something else, but whatever it is, it should be in slow motion, otherwise it would be impossible to understand). I guess the precession of our planet is not quick enough to be interesting in this context.
The new figure proposed by Brews (see above) is not good enough. It shows three successive (not simultaneous) rotations about fixed axes. Moreover, it refers to the concept of Euler Angles. I strongly suggest to leave this concept out of this article, if possible. Centrifugal force is already a difficult topic. Let's spare the readers additional doubts. Paolo.dL (talk) 21:03, 19 July 2008 (UTC)
[NOTE: The discussion about this topic started in a previous section. Paolo.dL (talk) 21:40, 19 July 2008 (UTC)
Paolo has deleted a note (quoted below), without discussion on this "talk" page, concerning the independence of one's choices for coordinate system and observational frame of reference:
Paolo's description of the rationale for this deletion on the "history" tab is : Coord. systems (CS) are strictly associated to reference frames (RF). RF, in physics, allow measurement of kinematic quantities. Cannot exist without a CS.
This rationale does not address the content of the deleted statement, which does not deny possible association of a reference frame to a coordinate system, but merely the plurality of this choice. In addition, the rationale is incorrect in that a reference frame can use vectors, which choice allows description of observations that are independent of any coordinate system.
Paolo's terminology "strictly associated" brings to mind Paolo's earlier remarks on the talk page. On the talk page Paolo suggested coordinate systems and observational frames of reference were the same thing. I answered with the excerpt below from earlier discussion, which Paolo did not address:
Additionally, the example of an "arc-length" description of motion by both the moving and stationary observers is discussed at length in the article and in more detail in other articles as already pointed out to Paolo in earlier discussion.
The short version of all this discussion is: Choice of coordinate system and choice of frame of reference are distinct and separable, one's choice of one does not limit the choice of the other. That is what the deleted Note says, and it should remain in the article.
I believe it is reasonable that an active issue on the talk page be given some attention on this page before being deleted. Brews ohare (talk) 13:50, 19 July 2008 (UTC)
I am sick of these repeated lies. For the second time, Brews wrote above, at the beginning of a new section, the phrase: "without previous discussion". The discussion about this topic began in a previous section, and has not finished yet. Here's my recent edit summary:
Coord. systems (CS) are strictly associated to reference frames (RF). RF, in physics, allow measurement of kinematic quantities. Cannot exist without a CS |
As I repeatedly pointed out previously, if two editors strongly disagree, the opinion of one of them cannot suddenly appear on the article, before an agreement is reached or at least the relative majority of the editors participating in the discussion agree! So, we should first discuss, hopefully with the help of others, then decide what we should write on the article.
Dear editors, can you see how many times I have to repeat this simple concept to Brews? Do you mind to help me to convince him? He likes to be a one-man-band. He is extremely talented, but Wikipedia is an orchestra. He perhaps deserves to be the prime violin, but should not be allowed to be a one-man-band. Please help me. Aren't there administrators in this group? Aren't there editors interested in symphonic music? Paolo.dL (talk) 22:02, 19 July 2008 (UTC)
I know, and I will reply, of course. But, as I repeatedly pointed out, the main problem with you is another. You behave as the owner and treat others as guests. This makes cooperation too hard. The same happened when we discussed the gyroscope example (see previous section). Please remove again your controversial sentence about CS and RF, and wait for this discusion to end. Paolo.dL (talk) 22:15, 19 July 2008 (UTC)
Brews, yes we are. I am convinced that your opinion about this topic is absolutely wrong, and the paragraph in the article expresses your own opinion. You need to admit that there are only two ways to be peer:
Now, would you mind to just guess what is the only one of these two possibilities which does not break Wikipedia policies? Another question: would you accept to keep my opinion on the article, if you were convinced it was wrong? Paolo.dL (talk) 21:00, 20 July 2008 (UTC)
And I do think you are wrong. So, at least in this respect we are peers. I do things one at a time. First, I want to convince you to work as a peer, not as the owner of this page. What is the only one of the above listed two possibilities which does not break Wikipedia policies? 1 or 2? Paolo.dL (talk) 22:29, 20 July 2008 (UTC)
The main issue under discussion here is that you want to impose your opinion. This is against Wikipedia policies. Your opinion will be expressed on the article if and only if we will agree or somebody else will "vote against me". Right now, your opinion has exactly the same weight as mine. If you agree on this rule, we will continue our discussion and you will possibly be able to prove you are right. I accept discussion only on a peer-to-peer basis. This is extremely important to me, and I hope that somebody else will help me to let you understand the importance of this principle. Paolo.dL (talk) 22:54, 20 July 2008 (UTC)
This talk page is becoming very long. Please consider archiving.
I don't know why gyroscopes are getting discussed on these pages. Gyroscope theory as per the textbooks involves neither centrifugal force nor Coriolis force.
My own personal opinion however is that the Coriolis force is heavily involved in gyroscope theory and that it is the reason why pivoted precessing gyroscopes don't topple over.
I have studied the official Lagrangian explanation in the textbooks in the greatest detail and I find it totally lacking as regards explaining why pivoted gyroscopes don't topple. There must be an extra force involved and it must take the form of vXω. This extra force is denied by modern physicists.
At any rate, all discussions about gyroscopes should be removed away from these pages and unto the Coriolis force pages.
We should be re-introducing the elliptical planetary orbit topic which is heavily related to centrifugal force.David Tombe (talk) 12:50, 20 July 2008 (UTC)
It's true that Coriolis Force has no equivalent potential energy. It's also true that Coriolis force acts perpendicularly to the direction of motion and so it only acts to change the direction of a velocity and not the speed. Hence kinetic energy is conserved under the action of a Coriolis force.
However, centrifugal force also only acts perpendicularly to the direction of the motion.
Furthermore, any actual potential energy involved in examples of centrifugal potential energy are actually gravitational potential energy or hydrostatic pressure. We are witnessing centrifugal kinetic energy being converted into some other kind of potential energy.
In fact the so-called expression for centrifugal potential energy given in the article is in reality merely a kinetic energy term. The kinetic energy of rotation merely converts to potential energy of another kind. In that respect we can loosely refer to it as a centrifugal potential energy.
Centrifugal potential energy as such does not exist. Centrifugal force and Coriolis force stand in an identical situation in this regard as they are merely mutually perpendicular aspects of the same thing. David Tombe (talk) 14:56, 20 July 2008 (UTC)
OK Brews, let's go inside a rotating bucket of water. The water surface is curved up the sides of the bucket due to centrifugal force. Every element of water is co-rotating with the rotating frame. The centrifugal force is exactly perpendicular to the motion of every element of the water.
We're back once again to your denial of the fact that something needs to be co-rotating in order to experience centrifugal force.
So let's then consider a rotating bucket in which the water is not co-rotating. The water surface will be level. There will be no centrifugal force and no potential energy. In fact this is exactly the famous Bucket argument.
I can assure you that centrifugal force is always perpendicular to the motion that causes it just like Coriolis force and just like F = qvXB in electromagnetism.
David: you have twice removed the phrase in italics from the sentence: "The Coriolis force has no equivalent potential, as it acts perpendicular to the velocity vector and hence rotates the direction of motion, but does not change the energy of a body." While this is not the only way of explaining why the Coriolis force has no associated potential while the centrifugal force does, it is a true statement (as you yourself have acknowledged), and you have not provided a good reason to remove it.Rracecarr (talk) 21:28, 20 July 2008 (UTC)
Paolo.dl, If an object is stationary in the inertial frame, it will trace out a circle as viewed from the rotating frame. There will be absolutely no radial motion. So how can there be any centrifugal force? The expression for centrifugal force involves the tangential speed of the particle in question. If that tangential speed is zero, how can there be any centrifugal force?
So if an object is not co-rotating in a rotating frame, it will not experience any centrifugal force.
Just take a look at a stationary bucket of water from a rotating frame centred on the axis of the bucket. Does that make the water climb up the walls? No. So there is no centrifugal force and no centrifugal potential energy. David Tombe (talk) 01:07, 21 July 2008 (UTC)
RRacecarr, you can't go storming in and reverting other peoples' edits and then come here stating that you are not willing to discuss the issue.
You have been advocating that centrifugal force and Coriolis force are both fictitious. Yet you are now claiming that while Coriolis force has got no associated potential energy, centrifugal force nevertheless has an associated potential energy which can cause rotating water to climb up the side walls of a bucket.
There are alot of matters connected with both centrifugal force and Coriolis force which you need to take a closer look at.
The section on centrifugal potential energy contains a contradiction which needs to be resolved. You know fine well that the water in the rotating bucket is moving perpendicularly to the centrifugal force. So you can't then go on and cite the fact that Coriolis force doesn't have a potential energy because it is perpendicular to the direction of motion.
Something in that section needs to be changed.
Either,
(1) the last sentence needs to be removed. Or,
(2) The last paragraph needs to be removed to the Coriolis force page and the rest of the section either deleted or entirely re-worded.
I would opt for the latter and re-word the remainder of the article to the extent that the term 'centrifugal potential energy' is really only a measure of rotational kinetic energy.
The stored energy in the rotating bucket is actually gravitational potential energy. It is not centrifugal potential energy. However it comes about as a result of the conversion of some rotational kinetic energy into gravitational potential energy as a result of centripetal force acting against the centrifugal force. So loosely we might say that the stored gravitational energy is centrifugal potential energy.
A similar situation can indeed occur with Coriolis force. A channel of water flowing along a radial drain pipe on a rotating turntable will have a similar gravitational potential energy as a result of the water being force up one side of the pipe tangentially.
And finally I should point out that according to your artificial circle theory which I totally disagree with, a Coriolis force acts radially inwards on stationary objects in the inertial frame, as viewed from a rotating frame. It has twice the magnitude of the centrifugal force and it takes on the same expression but with a factor of two, ie. 2mrω^2. Nonsense as this is, it is the core of the entire belief system of all the other active editors here. And on this basis, we can indeed construct a potential energy term from which to take a gradient and derive the Coriolis force.
So your entire belief system is totally confused and self contradictory.
If you are going to assume the role of unofficial guardian of the centrifugal force and Coriolis force pages, then you will need to learn to enter into constructive debate.
So far you have been relying entirely on your trump card which is that you have a large group of administrators who you can depend on to back you up in any edit war. David Tombe (talk) 10:24, 21 July 2008 (UTC)
No RRacecarr, You're the one that doesn't listen. I discuss things on the talk pages. I then make edits. You revert and then wrongly accuse me of not discussing it all first. Then when we go back to the talk pages you declare that you are not going to discuss anything.
This is because you operate in the full knowledge that you have a team of administrators behind you who will back you up everytime. This encyclopaedia operates on the principle of personality politics.
I have just noticed yet another flaw in the article. You state that Coriolis force is not position dependent. Yet your artificial circle theory depends on an expression for Coriolis force that is position dependent.
Your entire understanding of centrifugal force and Coriolis force has not been thought through properly. David Tombe (talk) 14:14, 21 July 2008 (UTC)
Wolfkeeper, you have just demonstrated to everybody that you can't see the difference between a rotating bucket of water in which the water climbs up the side walls, and a stationary bucket of water in which the surface is level.
You have tried to use specious mathematical arguments to convince us all that the two scenarios are exactly the same. David Tombe (talk) 01:39, 23 July 2008 (UTC)
As usual you guys are bashing David Tombe and treating him badly. That is your typical behavior. You act like the thugs which you are. You still need to apologise to him for your past bad behavior. You didnt do that so you have shown you are really not civilized people. I am still waiting for that apology to David, when are you going to do it???72.84.64.6 (talk) 13:19, 23 July 2008 (UTC)
As noted under Talk:Centrifugal_force#Coordinate_systems_and_frames, Paolo has deleted a Note subject to question on this Talk page. He has repeatedly refused to discuss the validity of this disputed note, despite many examples and careful presentations by myself. His attitude is that he will eventually get around to discussing the matter, but it seems from his unwillingness to respond that may be some considerable time.
I would like to have an independent review of this matter. First, is there anything to dispute? As far as I can see Paolo hasn't got a leg to stand on. Maybe if he would explain himself, I could see he has a different perspective, but at present I just don't know what his objections can be. All we have so far from Paolo are some categorical, unsupported statements, and a refusal to engage in their discussion. Brews ohare (talk) 00:50, 21 July 2008 (UTC)
I'm a previously uninvoled editor. To be honest, I'm have a really hard time following this debate. I don't see what the real dispute is. Is it a matter of source citing? Is one WP:RS contradicting another? I see that you've posted three proposed edits in this section. It seems to me that Paolo's edit is the one that includes WP:OR by saying "in general use". I should point out that neither of the edits listed here has any sources, so at this point, accusations by either side of WP:OR are undefendable.
Assuming sources can be found to support the third proposed edit, I have some recommendations in regards to the actual wording. If I'm not mistaken, the difference between a coordinate plane and an "observational frame of reference" is the former always starts at the same point and in the same direction, and the latter is always relative...? I'm a math major and I'm having a hard time deciphering your meaning, that says something about the tone of the article I think. Additionally, the use of the word "obviously" in the last sentence is not only poor math writing (books with this word always frustrate people), but it violates words to avoid. I suspect including that word was meant more for Paolo's benefit than the readers'. AzureFury (talk) 16:57, 21 July 2008 (UTC)
I'm going to support ip 63.34.xxx.xxx (btw, please register a user name it makes it easier to recognize your posts) on this. The term present in equations in polar coordinates and the term present in rotating reference frames are two sides of the same coin. (i.e. they are terms coming from the non-trivial connection coefficients involved in calculating the acceleration.) I think this article should cover both. Especially, since there is a whole bunch of textbooks that don't really distinguish between the two. (Marion and Thornton is one of them.) I do however see problems in providing a unified definition of the two, that distinguishes them from other fictious forces. (TimothyRias (talk) 16:47, 4 August 2008 (UTC))
Hi Timothy: I'm left-adjusting the format of these comments so they are easy to find. The objective is not to describe a curve, but to describe a motion along a curve. Otherwise we are doing analytic geometry. not mechanics, and there is no "acceleration" and no "time dependence". If you track a motion, the kinematics of the motion must be referred to the osculating circle, a circle with time-shifting center in general, to determine the centripetal force in an inertial frame of reference. (See Curtis.) This centripetal force becomes the centrifugal force in the non-inertial frame of motion attached to the moving particle. See here. Brews ohare (talk) 15:34, 5 August 2008 (UTC)
Hi Timothy: If you track motion, the motion is time dependent. And then the polar coordinates describing the motion are time dependent. (See here.) Brews ohare (talk) 15:34, 5 August 2008 (UTC)
Hi Timothy: I have no ambition to discuss relativistic formulations. I'll bet Marion and Thornton don't do that either, in this context, eh? Brews ohare (talk) 15:34, 5 August 2008 (UTC)
Hi Timothy: Well, in the big picture, maybe everything is connected. But within the framework of this corner of mechanics, with the usual definition of inertial frames (Lorentz or Galilean related), there is no basic connection; only an accidental connection in the case of circular motion. (The source of this accident already was described here.) Brews ohare (talk) 15:34, 5 August 2008 (UTC)
Hi Timothy: Sorry for the appearance of condescension. I am just trying to explain things from a certain (apparently limited) viewpoint. However, this narrow perspective is the one commonly adopted for this topic. Brews ohare (talk) 15:34, 5 August 2008 (UTC)
Stommel and Moore p. 4 "Sometimes the additional terms in the accelerations are transposed to the right side of the equation, leaving only the double-dotted terms on the left. So the acceleration terms on the right look like forces. They even acquire names such as "centrifugal force." As convenient as this may be from an intuitive, practical point of view, this transposition...can lead to confusion. ...So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system. p. 26: "you should be very clear in your mind not to confuse the idea of a plane polar coordinate system fixed in inertial space with the idea of rotation of coordinates. This chapter is entirely tied to one particular reference frame, fixed in inertial space – so don't get mixed up now, or later when we introduce rotating axes." p. 36: This immediately gives the components of acceleration in polar coordinates, [lists equations] Remember once again that all this has nothing to do with rotating coordinate systems. We are in a polar coordinate system that is at rest with respect to the stars....The term r ω2 then looks like a force, and it actually has a name: "the centrifugal force". ... But it is really not a force at all, and so if we want to make use of it in a formal sense, then we could call it a virtual, fake, adventitious force." Following these various cautions, these authors later proceed to a rotating frame (p. 54) where they again introduce polar coordinates, these now are polar coordinates in a rotating frame, and derive what is now the true fictitious force by analogy with the formulas for the polar coordinates in a stationary frame. They rely upon their earlier cautions about confusion, but (in my view) have done things in the way most likely to actually cause confusion. Nonetheless, they are perfectly clear that the two cases are different, and that they are exploiting a mathematical analogy.
I was unable to access the second source: "Statistical Mechanics" By Donald Allan McQuarrie. Brews ohare (talk) 17:13, 7 August 2008 (UTC)
As a correction, the Stommel and Moore reference was not mine, it was provided by Tim (Actually, it wasn't mine either, but the noname ip 63.something. (TimothyRias (talk) 12:02, 8 August 2008 (UTC))). Having said that, it's a fine reference, explicitly refuting your claims and confirming mine. By the way, I enjoyed your statement that when they discuss rotating coordinates they "derive what is now the true fictitious force", presumably as opposed to the false fictitious force that they derived for curved spatial coordinates, and had the nerve to call "centrifugal force". Let me just conclude this comment by repeating from your quotation: "So remember that the appearance of this type of unreal force does not necessarily involve a rotating coordinate system."Fugal (talk) 18:37, 7 August 2008 (UTC)
Surely you are joking MR Wolfkeper. I didnt think humor was allowed. Maybe you are simply being dishonest in order to prove that what I said previously is true. You do treat Mr Tombe with disrespect. In any event, I cant see nothing wrong in repeating what has been said by Mr Tombe, concerning which you now seem to be agreeing with Fugal, when he says basically the same thing. "Citations are being ignored when it suits certain editors".
<duplicate of suspended user screed deleted>- (User) WolfKeeper (Talk) 15:39, 10 August 2008 (UTC)
It seems to me that Mr Tombe has been right all along and you simply just ignored and opposed his correct viewpoint, which now you seem to be agreeing with, since it is being advocated by a different editor. I certainly would like to know if you are now agreeing with Fugal and conceeding that he is right so that we can continue to complete this article?71.251.182.49 (talk) 12:27, 10 August 2008 (UTC)
Sir, here you are attacking Mr Tombe, and that is not the point of this discussion. But if you seek to prove my point, I thank you for it. You have done so. You deliberately assume bad faith on the part of Mr Tombe, and so you have harassed him and unfairly blocked him and smeared his reputation. You continue to do that here by dead horse beating Mr Tombe who is unable to reply to your slanders. I think it is you who is being dishonest. You should frankly admit you have been wrong in this debate, and that Mr Tome and Frugal are correct in what they have said here. You and your supporters can then withdraw and let the article be completed without your blocking its progress towards completion.72.64.46.35 (talk) 20:55, 10 August 2008 (UTC)
Centrifugal effect redirects here. It's not a psychological effect (they're offtopic here anyway), it's an apparent acceleration in rotating reference frames, in the same way that coriolis effect is.- (User) WolfKeeper (Talk) 18:34, 3 August 2008 (UTC)
A radical suggestion: I propose that this article be moved to Fictitious forces in rotating frames, and that Coriolis force and Euler force be merged into it at the same time.
Rationale: the three "rotational" fictitious forces are all generated by the same physical phenomenon, and drop out as individual terms when the frame-transformation equation is differentiated and expanded. A detailed treatment of centrifugal force must necessarily include both of the others, and vice versa, and as a result both the Coriolis and Euler forces are already dealt with in this article.
After the merge we would thus end up with a single long fully-integrated article instead of one long article and two short ones with overlapping topics. Refactoring and copyediting work could then be more effectively applied to that single article, which I believe can be significantly shortened if a more general treatment is used, without treating centrifugal force as a special case that is separable from the other force terms.
At the same time, there are other related phenomena such as centripetal force and reactive centrifugal force and certain "centrifugal" terms in coordinate transformations which are not fictitious forces and not related to rotating frames, but are often confused with the rotational fictitious forces. Renaming this article will also make clear that the only topic being discussed is that of fictitious forces in rotating frames -- The Anome (talk) 12:11, 5 August 2008 (UTC)
User history indicates that you The Anome were actively editing during the adversarial phase in question. Did you make any attempt to control the adversarial expansion of the article? 86.141.250.16 (talk) 19:45, 10 August 2008 (UTC)
As a measure to limit useless debate over the proper content of the present page, I propose that the present centrifugal force page be renamed centrifugal force (classical mechanics) and new pages be started centrifugal force (general relativity), centrifugal force (polar coordinates) that are referred to by a disambiguation page: For the commonly used term centrifugal force and for the term as used in classical mechanics, see centrifugal force (classical mechanics). For the term as used as a mathematical convenience in polar coordinates, see centrifugal force (polar coordinates). For a very general approach useful to those with a background in general relativity see centrifugal force (general relativity).
Personally, I expect the other pages to develop very slowly as the main debaters on these issues have no real interest in contributing pages, and probably cannot bring enough muscle to bear to write these pages themselves. Brews ohare (talk) 15:27, 8 August 2008 (UTC)
Feel free to check these to make sure I've classified them correctly, and do your own googles or other kinds of searches.- (User) WolfKeeper (Talk) 00:00, 10 August 2008 (UTC)
< outdent ------------------------
Quite frankly, the more I look at this, the better having more articles looks. Some people have called this fragmentation, and perhaps expect that there would be massive duplication, but in reality that rarely happens, the hypertext nature of the wikipedia makes it easy to link to where detailed treatments are. There's also the user-centered point that people are usually looking for a particular topic that is for them, at their current education level and purposes, and right now we've not catered well to those different levels, and using a more general definition in this article would only make that worse, generality always implies greater complexity, even if it ultimately looks simpler.- (User) WolfKeeper (Talk) 12:48, 12 August 2008 (UTC)
Fugal characterizes the view of the present article that centrifugal force is a concept of physics is "original research". That arbitrary statement is rejected by all the citations in the article. There also is another meaning for "centrifugal" sometimes introduced in the limited context of polar coordinates as a mathematical device in that coordinate system. This different usage also is recognized in the article, but is obviously not the subject of the article. A full discussion of this other use is in the article on polar coordinates. What else needs to be said? Do we need a google search to count usages for each interpretation? This article is about the physics, not about math. Does an article on bridgework refer to the Golden Gate?
According to Fugal: "If the basis vectors of a coordinate system change in time, you call the resulting terms appearing in the equations of motion "physical", whereas if the basis vectors of a coordinate system change in space, you call those same terms arising in the equations of motion "mathematical"." And in later discussion, Fugal says: "…those that think only when the basis vectors change with time can the accelerating terms properly be called fictitious forces, and those who think it is just as legitimate to regard as fictitious forces terms arising from the basis vectors changing in space.". This characterization is incorrect. The contrast is not between different types of coordinate system (time varying vs. space varying, or whatever), but between a coordinate system (which provides a mathematical description of observations in space and in time) and a state of motion; and how that state of motion affects one's observations. Thus, an observer in an inertial frame can use a polar coordinate system, and so can an observer in a non-inertial frame. And both also can avoid doing so altogether and use Cartesian coordinates, or arc-length coordinates, or use vector analysis. Whatever approach they choose to describe their observations, it may be pointed out, the inertial observer finds only "real" forces enter Newton's laws of motion (forces that originate between physical bodies), while the non-inertial observer finds it necessary to add fictitious forces, among them the (physical) centrifugal force of this article. That (physical) centrifugal force is not the so-called "fictitious force" of mathematical manipulation. The so-called "fictitious force" of mathematical manipulation occurs for either observer if they choose polar coordinates, and is an artifact of polar coordinates, not a consequence of the state of motion of the observer. If citations are needed to support these explanatory remarks, please see the article proper.
As a mathematical point, the acceleration in polar coordinates is
The term is sometimes referred to as the centrifugal term as a mathematician's idea of picturesque vocabulary. In this equation, one component points in the radial direction (unit vector ) and the other component in the direction normal to this one (unit vector ). These two directions are not along and normal to a particle's trajectory except in unusual cases, such as circular motion about a fixed center coinciding with the origin of the polar coordinates. However, the (physical) centrifugal force (from the particle's viewpoint) is always normal to the particle's trajectory; in general, not in direction . Consequently, regardless of the mathematical conceit that the polar equation terms include a "centrifugal term" that terminology is at best poetic license from a physical context based upon the moving particle. Of course, if the polar coordinate system is that of an inertial observer, there is in fact zero (physical) centrifugal force; despite whatever the mathematical conceit chooses to call "centrifugal"; rather, there is a (physical) centripetal force, which is normal to the path of the particle, and not directed toward the center of polar coordinates; that is, unrelated to either term in the mathematical expression for acceleration above. Again, the mathematical conceit is only poetic license.
Again, none of this explanatory material is controversial. For citations, see the articles on polar coordinates, centripetal force, fictitious force and of course centrifugal force. I have had a lot to do with these articles, but I am not citing myself: rather, I'm suggesting you look up the citations in these articles.
Although planar polar coordinates are used in the mathematical example above, the same ideas apply to spherical or cylindrical coordinates. Only the form of the mathematical terms alters; the variously identified, mathematically picturesque "centrifugal" terms still are at best only very indirectly related to the (physical) centrifugal force, except for particular trajectories. Brews ohare (talk) 19:21, 10 August 2008 (UTC)
Brews this assertion of yours: Of course, if the polar coordinate system is that of an inertial observer, is somewhat illustrative of the argument here. The thing is polar coordinates do not necessarily refer to an inertial frame.(TimothyRias (talk) 08:46, 11 August 2008 (UTC))
As I've explained above the physical notion of a frame is inherently local. (this is somewhat obscured by the Poincare symmetry of flat space but is also true in flat space.) Besides an global choice for an inertial frame, you can also make a other natural choice for the local frames. I like to refer to this as the "Muslim" frame choice, namely the one that is always oriented in the direction of a central point (Mecca), in this choice the centrifugal term in the polar coordinates gets a very clear physical interpretation as the centrifugal force. As for your assertion that the centrifugal term in polar coordinates "only arises as a result of mathematical differentiation." Yes, thats true, but the same is true for the centrifugal term in a rotating frame of reference. The centrifugal force always arises as extra terms introduced in the covariant derivative. (TimothyRias (talk) 08:46, 11 August 2008 (UTC))
We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted , is said to move with the observer.… The spatial positions of particles are labelled relative to a frame by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame , can be considered to give a physical realization of . In a frame , coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.
— Jean Salençon, Stephen Lyle Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9
and from J. D. Norton:[2]
…distinguish between two quite distinct ideas. The first is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events in spacetime neighborhoods. The second, the frame of reference, refers to an idealized system used to assign such numbers … To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions. … Of special importance for our purposes is that each frame of reference has a definite state of motion at each event of spacetime.
— John D. Norton: General Covariance and the Foundations of General Relativity: eight decades of dispute, pages 835-836 in Rep. Prog. Phys. 56, pp. 791-858 (1993).
Assuming it is clear that "state of motion" and "coordinate system" are different, it follows that the dependence of centrifugal force (as in this article) upon "state of motion" and its independence from "coordinate system", while the mathematical version of "fictitious force" has exactly the opposite dependencies, indicates that two different ideas are referred to by the same terminology. The present article is about one of these two ideas, not both of them.
In summary, the article has focussed on the physical view based upon "state of motion", while Timothy and Fugal are more focussed on the mathematical manipulations within a curvilinear coordinate system, independent of the observer's state of motion. Some arguments given are more or less correct from one stance, some from the other, but the article quite properly treats the usual "state-of-motion" meaning, and refers the other to the appropriate mathematical treatment of whatever coordinate system you might like to pick, e.g. polar coordinates.
I have rewritten the section on "Aside on polar coordinates" in a way that I hope meets everybody's approval.
((cite book))
: |page=
has extra text (help)
Brews ohare (talk) 16:54, 13 August 2008 (UTC)
There is something wrong with the following line introduced in one of the recent edits (at the end of first paragraph of the "Centrifugal force in general curvilinear coordinates" section):
This attempt at a general definition seems to fail to include the case of a rotating reference system (the one case we all agree is the most commonly treated one), in which the centrifugal force is not necessarily normal to the trajectory of a particle. It would also include the coriolis force in such a case, since that is always perpendicular to the particles velocity. (well as long as the particle is moving in a plain perepedincular to the axis of rotation, anyway.) The sentence cites a source which I haven't been able to check. But I highly doubt that this sentence is conveying what that text was saying. (TimothyRias (talk) 14:00, 14 August 2008 (UTC))
The way this new section was introduced has a number of shortcomings, as does its content.
As to its manner of introduction, it was placed on the page without any discussion on this talk page, despite a very careful attempt on my part to resolve a number of issues on this page. My efforts, involving a simply stated contrast of views, my citations supporting these views, and my attempt to resolve these matters in a compromise, all were ignored entirely.
As to its content:
The subsection states:"This article is primarily concerned with the view of centrifugal force (and other fictitious forces) presented in introductory texts, which typically rely on intuitive though somewhat imprecise notions of concepts such as reference frames, forces, observations, and so on. In more advanced and abstract treatments of dynamics, the definitions of all these things are more general and explicit." I interpret these remarks as a dismissal of all citations opposing the author's views, which citations are in fact very numerous and include major authorities in the field such as Arno'ld, Lanczos, Landau and Lifshitz, Born, Einstein, Newton, etc. This statement is an unsupported and unsupportable slap at most of the texts on the subject, and should be deleted.
The article states: "In particular, an inertial coordinate system is defined as a system of space and time coordinates x1, x2, x3, t in terms of which the equations of motion of a particle free of external forces are simply d2xj/dt2 = 0.[51] " This definition of an inertial frame is not that of special relativity or of Newtonian mechanics. A clear counterexample is simply a frame moving with an accelerating particle: in this frame the second derivatives of position of this particle are all zero, but no-one would call this an inertial frame. The reference provided for this incorrect viewpoint is [Friedman] without page number or quotation. Given this editor's proclivity for taking things out of context, and given the clear citations for the contrary standard definition at inertial frame, this revisionist version of "inertial frame" should be removed from the page.
The article states "When equations of motion are expressed in terms of any non-inertial coordinate system (in this sense), extra terms appear, called Christoffel symbols." It is not helpful to introduce out of the blue an advanced concept like Christoffel symbols without explanation (or definition). Also, this article is not the place to introduce these technicalities, which belong (if they do belong) in a more technical article devoted to the subject of dynamics in curvilinear coordinates. It might be noted that a very large fraction of books on this subject, advanced and simple, never even mention Christoffel symbols, which apparently are not critical to the subject of centrifugal force.
The article states "Strictly speaking, these terms represent components of the absolute acceleration (in classical mechanics), but we may also choose to continue to regard d2xj/dt2 as the acceleration (as if the coordinates were inertial) and treat the extra terms as if they were forces, in which case they are called fictitious forces.[52] " The Christoffel symbols are connected to "forces" only in the limited mathematical sense of reinterpretation of mathematical terms by moving them from one side of the equation for acceleration to another, and have absolutely no connection to the state of motion of the observer. The reference cited says nothing about Christoffel symbols, and simply points out that the "mathematical device" of transferring terms from one side of an equation to the other can be described as introducing "fictitious forces". These authors are very, very careful to distinguish between the interpretation of this device in an "inertial frame" and its interpretation in a rotating frame. These sentences in this subsection distort the position of the cited source, and should be removed.
The article states "The component of any such fictitious force normal to the path of the particle and in the plane of the path’s curvature is then called centrifugal force.[53]" Timothy has objected to this statement, and Fugal's support for this statement is (i) a quotation stripped from context and (ii) some unsupported remarks about Christoffel symbols and (iii) some remarks about ambiguity and "absolute significance" in the case of circular motion that are nonsense. One problem with this sentence is that what is called centrifugal force depends on the state of motion of the observer of the particle, and so cannot be categorically given a unique definition independent of the observer.
The subsection also contains incomplete references (no links, isbn's, or page numbers), mainly to subsidiary topics (like curvilinear coordinates as an abstract mathematical topic, unrelated to physics) that are peripheral to the main thrust of the arguments. There are no definitions of terms and notation, and equations are poorly formatted.
I have removed this subsection. Before it is reintroduced, I suggest a return to the discussion opened on the talk page under the heading "#Fugal's positions", where simple courtesy demands formal response. At a minimum, there must be a proper discussion of the issues. Brews ohare (talk) 15:51, 15 August 2008 (UTC)
I think it might be helpful to get some fresh perspectives on this article. Several people have suggested that two individuals are showing signs of "ownership", and I have to agree. It seems that two editors have a very specific idea of exactly what this article must say, no more and no less, despite well sourced inputs from other editors. These two editors have made edits when opposed by the majority of other editors, and have repeatedly claimed ownership of this article (pointing out that THEY created it, THEY put the work into it, so any other views MUST go into other articles, not this one.) How does one go about requesting mediation in cases such as this? Fugal (talk) 21:40, 15 August 2008 (UTC)
As a case in point, note the latest challenge from one of these owners: "If it can be referenced (and please make it a good reference to a factual way that this is true, rather than somebody talking hyperbolically in a book..." I think this gives a good idea of what is going on here. Since numerous references from the most reputable published sources have been provided for the views that this editor wishes to keep out of the article, he now demands that a reference be provided, but not just "somebody talking hyperbolically in a book". I think that speaks for itself. Clearly this editor will not accept any view that differs from his pre-conceived views. He simply dismisses all published works from reputable sources as "somebody talking hyperbolically in a book". And this is the more reasonable of the two owners. Some kind of mediation is badly needed here.Fugal (talk) 21:49, 15 August 2008 (UTC)
I have attempted to eliminate erroneous concepts that fail to distinguish between coordinate systems and reference frames. Quotations with relevant citations are given earlier on this talk page, and Fugal has been invited several times to comment. (For example, see Fugal's positions, and Fugal's sources). All the math and the statements made in the new article are non-controversial and are supported in mathematical detail by the citations. Brews ohare (talk) 22:45, 15 August 2008 (UTC)
In this connection, I suggest that the links to Stommel and Moore be followed and the work read closely. These authors are very, very careful to distinguish the cases of polar coordinates in inertial frames from that in non-inertial (rotating) frames. For example:
OK, we're still battling the scope issues I think.
The disambiguation page has 4 different definitions:
I'm hoping that this classification is fairly non controversial (although other people may want to add other examples of centrifugal force as well perhaps, and by all means).
I would like to move this (Centrifugal force) article to Centrifugal force (rotating reference frame) and I would propose to leave a redirect to it from Centrifugal force. This better clarifies for the users what the article is about in the name, and gives us more flexibility to change things if that should be decided later. It also gives us a specific name to link to from Coriolis effect that refers directly to the associated type of centrifugal force that that article is associated with.
I'm hoping that this too is relatively non controversial, but I welcome comments. I feel that there are people who wish to put a more general article at Centrifugal force, if anything this renaming should make that easier to do later if this type of article were created and there was consensus to change the redirect.- (User) WolfKeeper (Talk) 22:57, 15 August 2008 (UTC)
While the curvilinear coordinates can be seen as a generalisation of the rotating reference frame, the polar coordinates section talks only about inertial frames of reference. It therefore isn't the same centrifugal force, and very probably needs to go.
The difference is obvious- if an object is stationary in polar coordinates, then there is no centrifugal force. In a rotating reference frame, there is a centrifugal force when the object is stationary. They are not the same thing at all, and the associated coriolis forces are completely different also, they act in different directions and are of different magnitudes.
More or less polar centrifugal force is to rotating reference frame centrifugal force as the magnetic force is to electrostatic force. And they are special cases of curvilinear equations and electromagnetism, respectively.
Magnetism and Electrostatics have almost the same form of equations, but they are completely different in reality, and the same thing applies here. Too many people aren't really getting this. Similar mathematics is just not enough.
Just like I don't think we would really want a big section on magnetism in an electrostatics article, we don't really want a big section on polar coordinates in a rotating reference frame article.
But we also don't really need too much on general electromagnetism in a magnetic article either, the curvilinear stuff is a bit OTT at the moment, it needs to mostly go in its own article, but in my opinion having something here is quite valid.- (User) WolfKeeper (Talk) 02:40, 16 August 2008 (UTC)
Wolfkeeper: You do not seem to have read my comments upon this wording when it first appeared. There are defects that must be fixed. Whether or not you have taken the time to really look at it, this section contradicts some very basic facts, and is completely opposite to much of what is said in the Polar coordinate version, which is, after all, a special case of curvilinear coordinates. It also only appears to have citations, as many of the citations apply only to peripheral matters and do not document what is asserted in the sentence they are attached to.Brews ohare (talk) 16:03, 16 August 2008 (UTC)
This section has been completely rewritten and the relevant math included. An excellent exposition by Silberstein with a full view on google straightens out the entire mess. Brews ohare (talk) 15:41, 17 August 2008 (UTC)
I find the difference being made made between "coordinate" and "state of motion" fictious forces being made in this article to be somewhat artificial. It seems to complete ignore the fact both just define a particular frame. (Or rather tetrad as the properly defined concept is called.) (TimothyRias (talk) 10:00, 18 August 2008 (UTC))
First of all let me point out that "state of motion" alone is not enough to get centrifugal force even in a rotating frame, an orientation also needs to be specified. (An easy example of this is given by the origin in a rotating frame. Its state of motion is "stationary", centrifugal force is caused by the fact that the orientation of the origin is continuously changing (with respect to the orientation defined in an "inertial" frame). Specifying a "state of motion" and orientation at every point in space, is in fact specifying a tetrad.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))
A practical manner of assigning a tetrad is by first defining a coordinate system, and then using the coordinates basis at each point to define the tetrad. (This approach is commonly taken in GR.) An other approach, frequently taken in classical mechanics, is to assign assign "states of motion" everywhere but orientations only at one point in space, and using parallel transport assisted by flatness of space to extend this orientation to the entirity of space. This approach leads to a choice of orientation that is independent of the choice of spacial coordinates. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))
We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". Let us give a more mathematical definition:… the reference frame is... the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted , is said to move with the observer.… The spatial positions of particles are labelled relative to a frame by establishing a coordinate system R with origin O. The corresponding set of axes, sharing the rigid body motion of the frame , can be considered to give a physical realization of . In a frame , coordinates are changed from R to R' by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.
— Jean Salençon, Stephen Lyle. (2001). Handbook of Continuum Mechanics: General Concepts, Thermoelasticity p. 9
For polar coordinates these approaches lead to different choices of frame. Insisting that these frames are "straight" leads to the inclusion of fictious forces in the first while it does not in the second. Brews has systematicly tried to label this difference as purely mathemtical, while in fact it is the direct result of the very physical choice of frame. (well, at least just as physical as the choice between a rotating and an inertial frame.)(TimothyRias (talk) 10:00, 18 August 2008 (UTC))
Now, does this make the centrifugal force in a rotating frame and the one in the polar coordinate frame the same? Yes and No.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))
Clearly they appear in different choices of frame, hence they are different. Yet, they arise as a result of the same physical reasoning (they are both fictious forces resulting from think of a "nonstraight" frame as "straight") and are both "outward pointing", making them very similar. With the difference and simularities being so subtle most textbooks choose the circumventing the issues (or just plain ignore it and just label both as "the" centrifugal force) adopting a "who cares where you put those acceleration terms, just put them somewhere and analyse the differential equations" additude.(TimothyRias (talk) 10:00, 18 August 2008 (UTC))
((cite book))
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has extra text (help)CS1 maint: multiple names: authors list (link) and Shuzhi S. Ge, Tong Heng Lee, Christopher John Harris (1998). Adaptive Neural Network Control of Robotic Manipulators. World Scientific. p. p. 48. ISBN 981023452X. ((cite book))
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has extra text (help)CS1 maint: multiple names: authors list (link)What does this mean for the wikipedia article? I see two options:
Some options that I think should be avoided:
I really wish that we can stop arguing so much about this. (TimothyRias (talk) 10:00, 18 August 2008 (UTC))
It occurs to me that the current article would be just fine if only it was given the more accurate name "Brews Ohare's Personal POV and Commentary on Centrifugal Force and Other Miscellaneous Topics". If this were the article's title, there would be much less dispute over the content, since it would be, by definition, whatever Brews wants it to be (although it might then be more appropriately hosted somewhere other than Wikipedia). The current article is brimming over with neoligisms like "coordinate fictitious force" and "state-of-motion fictitious force", and elaborate attempts to rationalize Brews' personal (and evolving) ideas about what these newly minted terms ought to mean. From the standpoint of Wikipedia, this article has become truly pathological, bloated to the point of being unreadable. And whenever someone makes the slightest attempt to modify it, they are bombarded with ten or twenty counter-edits from Brews, coupled with an equal number of interminable rants on the discussion page, where we are informed that his beliefs are "beyond controversy". Several people have suggested (independently) that Brews should relinquish ownership and take a much needed break, but he shows no signs of taking this advice. The entire article has become a novel narrative interwoven with original research and highly POV rationalizations, all aimed at trying to justify why Brews' somewhat naive and unsophisticated view of the subject is superior to all other views. This kind of exercise in polemics really isn't appropriate for a Wikipedia article (in my opinion).Fugal (talk) 13:39, 20 August 2008 (UTC)
((cite book))
: |page=
has extra text (help)The equations of motion in an non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.
— V. I. Arnol'd: Mathematical Methods of Classical Mechanics Second Edition, p. 129
An additional force due to nonuniform relative motion of two reference frames is called a pseudo-force.
— H Iro in A Modern Approach to Classical Mechanics p. 180
Comment by TimothyRias:
Let's do it a bit more explicitly. Suppose we have an inertial frame with cartesian coordinates x and y. (for convenience we drop de third coordinates). In this frame we can adopt new (time dependent) coordinates: (disclaimer any equations should be read module missing/extra signs)
If we do so we get the following acceleration:
We can introduce a "coordinate acceleration"
By which we introduce a coordinate fictitious force:
You will recognize these as the regular expressions for the fictitious forces in a rotating frame. However we are still an inertial frame, hence by definition (of fictitious force) these cannot be fictitious forces. Interpreting these as fictitious forces implies going to the corresponding rotating frame; the coordinate frame of the choosen coordinates. This is quite general, interpreting the extra acceleration terms in certain coordinates as fictitious forces always implies adopting the coordinate frame. When these extra terms are non-zero it also implies that the coordinate frame in non-inertial. The polar coordinate frame fictitious forces being non-zero when applying the coordinates to an inertial frame doesn't make them different from the rotating frame fictitious forces. The rotating frame fictitious are also non-zero if you apply the corresponding coordinates to an inertial frame. Hence the thing that you described above as a real difference that cant be ducked is a not difference at all. It is just a difference in the way you have been treating the two cases, but each treatment can be applied to both cases. (TimothyRias (talk) 09:09, 22 August 2008 (UTC))
1. Unless one adopts your view that calling certain acceleration terms in an inertial frame "fictitious" definitely implies ipso facto that a change of frame to a non-inertial frame is made, the idea that these terms are fictitious forces in the common meaning of that term (as per the quotations above from Arnol'd and Iro) is nonsense.
2. If a change to a non-inertial frame is implied, one must face the prospect that there are an infinity of non-inertial frames, and one must choose which one is implied . Thus, mere implication of the switch of frames is very ambiguous. It would be pertinent to specify which frame is implied.
3. If switching is implied, the variables must be redefined by implication as well. For example, using the fictitious force , the original meaning of the variables r, θ refer to the position of a moving particle, and are only indirectly related to the rotation Ω of any frame of reference (because the particle is moving in some curved path, it has its own angular velocity in any frame). This point is noted by Stommel, for example, who distinguishes between Ω and the full angular velocity of the particle dθ/dt .
4. No author that I can find has said either that a frame change is implied, or provided any guidance as to just what frame and what variable changes might be implied.
The current article is getting filled up with attempts to rationalize the personal POV of one editor. It appears to me (although I haven't taken a formal vote) that the majority of other editors believe the neoligisms and novel narratives being woven by that editor are not reflective of any published reputable source. To some extent, this is probably unavoidable, because the topic in dispute is not considered to be significant enough (or difficult enough) to warrant being discussed explicitly in very many reputable sources. Most scientists understand what Christoffel symbols mean, and the fact that none of them are "more physical" than the others, but they don't feel it necessary to make a point of this obvious fact.
Maybe the best way forward is to move the last half of this article, beginning with the discussion of polar coordinates, to its own article, which could be on the general subject of centrifugal force, allowing this article to be focused just on Brewsian centrifugal force in rotating coordinates. I seem to recall that Brews said not long ago that he advocated moving this "insignificant side topic" to its own article, where he felt certain it would languish for lack of interest. If I remember rightly, he said once it was move from his page, he didn't care what happenned to it. So he is presumably all in favor of my proposal.Fugal (talk) 01:36, 24 August 2008 (UTC)
Clear quotes from Arnol'd (an impeccable authority on the subject at a very sophisticated level) and Iro (a textbook, author's rep unknown to me, but a very standard statement) state that fictitious forces do not arise in inertial frames. No-one challenges these authors. On the other hand, there are very clear quotes showing that some authors have defined fictitious forces so they do exist in inertial frames. Among them are many in the area of design of robotic manipulators (for example, Ge et al. and Teshnehlab & Watanabe) and some standard works as well. Stommel, Shankar, and McQuarrie for example. What is there to argue about? Cited sources have used different meanings for the same terminology. All we can do is recognize the fact and point it out to the reader.
It seems to me that it is impossible to dispute the above facts. If dispute is attempted, it must show that in fact authors do not define fictitious forces that are non-zero in an inertial frame. Obviously, examples of this activity are already cited and cannot be made to go away. Brews ohare (talk) 17:46, 25 August 2008 (UTC)
((Disputed|date=August 2008)) ((very long)) I think these tags should be removed. The first tag was placed by Fugal, and the issues he raised have been dealt with in the section of the article linked here. (He hasn't signed off on them, but also has not responded to suggestions for further discussion.) The second tag was placed by Timothy, who has not explained what exactly is too long about it, or what to do about it, and seems continually to insist upon exploration of advanced issues, with a tenuous (or, at least, vaguely identified) relation to the subject, requiring a still longer article to explain technical jargon (e.g. "tetrads", "congruence of timelike curves defined by constant spacelike coordinates", "continuous specification of the orientation of a spacelike triad to the timelike vectorfield"). Brews ohare (talk) 17:09, 28 August 2008 (UTC)
OK, this article has grown way out of proportion. The current article size is over 100k. Not all of this is readable prose, but most of it is. (certainly at least 80k) We need to get this article back to readable proportions. Here are somethings that I think can be done to reduce the length:
(I'm out of time for the moment, I'll be back to elaborate on this last point some more.) (TimothyRias (talk) 10:31, 29 August 2008 (UTC))